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The Property of the Solutions of Higher Order Non-homogeneous Differential Equations in the Unit Disc

Zong-Xuan Chen

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Abstract

The higher order non-homogeneous differential equation in the unit disc was studied.Let f be the solution of non-homogeneous linear differential equation of higher order f(k)+Ak-1(z)f(k-1)+…+A0(z)f=F(z),the coefficients Aj(z)(j=0,…,k-1) and F(z)(not equiv 0)were analyzed in the unit disc,the relationship between the growth order of f and the growth order of F(z) under different conditions was elucidated.

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The higher order non-homogeneous differential equation in the unit disc was studied.Let f be the solution of non-homogeneous linear differential equation of higher order f(k)+Ak-1(z)f(k-1)+…+A0(z)f=F(z),the coefficients Aj(z)(j=0,…,k-1) and F(z)(not equiv 0)were analyzed in the unit disc,the relationship between the growth order of f and the growth order of F(z) under different conditions was elucidated.

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Available abstract

The higher order non-homogeneous differential equation in the unit disc was studied.Let f be the solution of non-homogeneous linear differential equation of higher order f(k)+Ak-1(z)f(k-1)+…+A0(z)f=F(z),the coefficients Aj(z)(j=0,…,k-1) and F(z)(not equiv 0)were analyzed in the unit disc,the relationship between the growth order of f and the growth order of F(z) under different conditions was elucidated.

Key concepts: Homogeneous differential equation, Homogeneous, Order (exchange), Unit (ring theory), Differential equation, Mathematics, Linear differential equation, Differential (mechanical device)

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